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6.1 Design and flow analysis of the turbine 83 tured grids: coarse grid having 6 480 cells, medium grid having 27 648 cells, and dense grid having 55 728 cells. The simulations were performed by using k − ω SST-turbulence model. The grid dependency is assessed by monitoring two parameters: the flow velocity in the mean line of the flow channel and the pressure distribution on the longer wall of the nozzle. Figure 6.4a presents the results of flow velocity in the mean line of the flow chan- nel and Figure 6.4b the results of pressure distribution on the longer wall of the nozzle. 350 300 250 200 150 100 50 0 −0.5 0 0.5 1 Lenght parameter, [−] Coarse grid Medium grid Fine grid 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 Lenght parameter, [−] Coarse grid Medium grid Fine grid (a) (b) Figure 6.4: Grid dependency study. Flow velocity in the mean line of the flow channel (a) and pressure distribution on the longer wall of the nozzle (b). The results show that the velocity magnitude and pressure distribution agree reasonably well when using medium and fine grid, and the solution is close to grid independency when using medium and fine grid. The general shape of the pressure peak, in a location where an oblique shock wave from blade trailing edge hits the longer wall, is similar be- tween the two densest grids even if the position is slightly different. This difference is considered to be acceptable, and hence, results calculated with the same grid but at dif- ferent operating conditions can be compared. Therefore, computational grids having the number of cells comparable to the number off cells used in the medium grid were used in the simulations for the studied stator geometries presented in the following sections. Different stator geometries having a similar throat width and blade height were simulated in turbine design operation conditions. The studied geometries represent slightly differ- ent nozzle setting angles, distances between the stator and rotor, and slightly different shapes of the diverging part of the nozzle. The design condition results for the studied stator geometries are presented in Table 6.4. In general, the simulated results show rea- sonably good agreement with the results obtained in the 1D turbine stator design. The stator outlet velocity and the Mach number predicted in the CFD simulations are slightly higher than the values used in the turbine 1D design. Based on the results presented in Table 6.4, the k − ω SST-turbulence model predicts higher flow outlet velocities when Flow velocity, [m/s] p /p , [−] st tot,inPDF Image | WORKING FLUID SELECTION AND DESIGN OF SMALL-SCALE WASTE HEAT RECOVERY SYSTEMS BASED ON ORGANIC RANKINE CYCLES
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